# Re: Fuzziness: what am I missing?

Anthony Cowden (cowden@sonalysts.com)
Mon, 6 Apr 1998 00:03:28 +0200 (MET DST)

Dimitri Lisin wrote:
>
> Yes, you are right, a fuzzy inferencing system is basically a mapping from
> a set of input variables to a set of output variables. And if it is
> possible to figure out a normal mathematical function that does the
> mapping, you don't really need it. FL is usefull, however, if you only
> have an intuitive understanding of the way the mapping should behave.
> With FL you can specify how the function *tends* to behave and get an
> approximation.
>
> What I want to know, though, is if you have a normal mathematical function
> given to you, how do you build a fuzzy inferencing system that best
> approximates it (for some given sampling)? I am trying to figure this out
> mathematically, but the math gets rather messy. Can anyone help?

Why would you want to do this in practice? Mathematical functions
(including fuzzy systems) are a symbolic way of representing something
else. Why would you want to represent a representation with another
representation? This only seems to remove you farther from the
problem. One of the nice features of fuzzy logic is that it tends to
move the function closer to the semantics underlying the descritpion of
the problem than most mathematical functions allow.

But I digress: most of the posts in this thread seem to be missing the
underlying basis of fuzzy logic, which is how fuzzy set membership
differs from traditional set membership, and how a logic based on
partial memberships differs from one that only allows for two
memberships.

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